My brake light turns on when I give my car some hard acceleration. Why does it do this, especially since my emergency break is down?:
This is a sign that your car is about to explode, sell it immediately.
Just kidding.
This is a clear sign that your brake fluid is low. Fill it, and you should be good to go. If this does not fix it, another reported solution could be to check the connector switch on the e-brake. You can readjust this by taking off the center console, and you then should be able to see the plate that the e-brake touches to make the light come on.
Oddly enough, a few members have also mentioned that under very hard acceleration, your e-brake might lift slightly (especially if it is loose), which also might trigger the light. Put some weight on it, tightening it, or even smoothing it in duct-tape could be the solution for this scenario.